On Regular Polytopes of 2-Power Order

Abstract

For each $$d\ge 3$$ , $$n \ge 5$$ , and $$k_1, k_2, \ldots , k_{d-1}\ge 2$$ with $$k_1+k_2+\cdots +k_{d-1}\le n-1$$ , we show how to construct a regular d-polytope whose automorphism group is of order $$2^n$$ and whose Schlafli type is $$\{2^{k_1},2^{k_2}, \ldots , 2^{k_{d-1}}\}$$ .